Parametrization of the Relativistic ($\sigma-\omega$) Model for Nuclear Matter

We have investigated the zero-temperature equation of state (EoS) for infinite nuclear matter within the $(\sigma-\omega)$ model at all densities $n_{\mathrm{B}}$ and different proton-neutron asymmetry $\eta\equiv(N-Z)/A$. We have presented an analytical expression for the compression modulus and found that nuclear matter ceases to saturate at $\eta$ slightly larger than $0.8$. Afterward, we have developed an analytical method to determine the strong coupling constants from the EoS for isospin symmetric nuclear matter, which allow us to reproduce all the saturation properties with high accuracy. For various values of the nucleon effective mass and the compression modulus, we have found that the quartic self-coupling constant $G_4$ is negative, or positive and very large. Furthermore, we have demonstrated that it is possible (a) to investigate the EoS in terms of $n_{\mathrm{B}}$ and $\eta$; and (b) to reproduce all the known saturation properties without $G_4$. We have thus concluded that the latter is not necessary in the $(\sigma-\omega)$ model.